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Added kernel regression

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master
Per.Andreas.Brodtkorb 13 years ago
parent a7a00851cc
commit 31f61eb319
1 changed files with 171 additions and 33 deletions
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202
pywafo/src/wafo/kdetools.py
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@ -189,8 +189,9 @@ class _KDE(object):
def _eval_grid(self, *args):
pass
def _eval_grid_fun(self, eval_grd, *args, **kwds):
output = kwds.pop('output', 'value')
f = eval_grd(*args, **kwds)
if kwds.get('output', 'value') == 'value':
if output == 'value':
return f
else:
titlestr = 'Kernel density estimate (%s)' % self.kernel.name
@ -223,7 +224,7 @@ class _KDE(object):
self.d)
raise ValueError(msg)
return points
def eval_points(self, points, r=0):
def eval_points(self, points, **kwds):
"""Evaluate the estimated pdf on a set of points.
Parameters
@ -244,9 +245,9 @@ class _KDE(object):
"""
points = self._check_shape(points)
return self._eval_points(points, r=r)
return self._eval_points(points, **kwds)
def _eval_points(self, points, r=0):
def _eval_points(self, points, **kwds):
pass
__call__ = eval_grid
@ -410,21 +411,10 @@ class TKDE(_KDE):
"""
return self._eval_grid_fun(self._eval_grid_fast, *args, **kwds)
# f = self._eval_grid_fast(*args)
# if kwds.get('output', 'value') == 'value':
# return f
# else:
# args = self.args
# titlestr = 'Kernel density estimate (%s)' % self.kernel.name
# kwds2 = dict(title=titlestr)
# kwds2.update(**kwds)
# if self.d == 1:
# args = args[0]
# return WafoData(f, args, **kwds2)
def _eval_grid_fast(self, *args):
def _eval_grid_fast(self, *args, **kwds):
if self.L2 is None:
f = self.tkde.eval_grid_fast(*args)
f = self.tkde.eval_grid_fast(*args, **kwds)
self.args = self.tkde.args
return f
#targs = self._dat2gaus(list(args)) if len(args) else args
@ -447,11 +437,11 @@ class TKDE(_KDE):
self.args = args
return fi*(fi>0)
return f
def _eval_grid(self, *args):
def _eval_grid(self, *args, **kwds):
if self.L2 is None:
return self.tkde.eval_grid(*args)
return self.tkde.eval_grid(*args, **kwds)
targs = self._dat2gaus(list(args))
tf = self.tkde.eval_grid(*targs)
tf = self.tkde.eval_grid(*targs, **kwds)
points = meshgrid(*args) if self.d > 1 else self.args
f = self._scale_pdf(tf, points)
return f
@ -632,7 +622,7 @@ class KDE(_KDE):
Xn = []
nfft0 = 2 * inc
nfft = (nfft0,)*d
x0 = np.linspace(-inc, inc, nfft0 + 1)
x0 = np.linspace(-inc, inc, nfft0+1)
for i in range(d):
Xn.append(x0[:-1] * dx[i])
@ -671,12 +661,11 @@ class KDE(_KDE):
d = len(grd)
for i in range(d):
grd[i] = grd[i].ravel()
r = kwds.get('r', 0)
f = self.eval_points(np.vstack(grd), r=r)
f = self.eval_points(np.vstack(grd), **kwds)
return f.reshape(shape0)
def _eval_points(self, points, r=0):
def _eval_points(self, points, **kwds):
"""Evaluate the estimated pdf on a set of points.
Parameters
@ -698,29 +687,124 @@ class KDE(_KDE):
d, m = points.shape
result = np.zeros((m,))
r = kwds.get('r', 0)
if r==0:
fun = lambda xi : 1
else:
fun = lambda xi : xi ** r
fun = lambda xi : (xi ** r).sum(axis=0)
if m >= self.n:
y = kwds.get('y', np.ones(self.n))
# there are more points than data, so loop over data
for i in range(self.n):
diff = self.dataset[:, i, np.newaxis] - points
tdiff = np.dot(self.inv_hs / self._lambda[i], diff)
result += fun(diff) * self.kernel(tdiff) / self._lambda[i] ** d
result += y[i] * fun(diff) * self.kernel(tdiff) / self._lambda[i] ** d
else:
y = kwds.get('y', 1)
# loop over points
for i in range(m):
diff = self.dataset - points[:, i, np.newaxis]
tdiff = np.dot(self.inv_hs, diff / self._lambda[np.newaxis, :])
tmp = fun(diff) * self.kernel(tdiff) / self._lambda ** d
tmp = y * fun(diff) * self.kernel(tdiff) / self._lambda ** d
result[i] = tmp.sum(axis= -1)
result /= (self._norm_factor * self.kernel.norm_factor(d, self.n))
return result
class KRegression(_KDE):
""" Kernel-Regression
Parameters
----------
data : (# of dims, # of data)-array
datapoints to estimate from
y : # of data - array
response variable
p : scalar integer (0 or 1)
Nadaraya-Watson estimator if p=0,
local linear estimator if p=1.
hs : array-like (optional)
smooting parameter vector/matrix.
(default compute from data using kernel.get_smoothing function)
kernel : kernel function object.
kernel must have get_smoothing method
alpha : real scalar (optional)
sensitivity parameter (default 0 regular KDE)
A good choice might be alpha = 0.5 ( or 1/D)
alpha = 0 Regular KDE (hs is constant)
0 < alpha <= 1 Adaptive KDE (Make hs change)
xmin, xmax : vectors
specifying the default argument range for the kde.eval_grid methods.
For the kde.eval_grid_fast methods the values must cover the range of the data.
(default min(data)-range(data)/4, max(data)-range(data)/4)
If a single value of xmin or xmax is given then the boundary is the is
the same for all dimensions.
inc : scalar integer
defining the default dimension of the output from kde.eval_grid methods (default 128)
(For kde.eval_grid_fast: A value below 50 is very fast to compute but
may give some inaccuracies. Values between 100 and 500 give very
accurate results)
Members
-------
d : int
number of dimensions
n : int
number of datapoints
Methods
-------
kde.eval_grid_fast(x0, x1,..., xd) : array
evaluate the estimated pdf on meshgrid(x0, x1,..., xd)
kde.eval_grid(x0, x1,..., xd) : array
evaluate the estimated pdf on meshgrid(x0, x1,..., xd)
kde.eval_points(points) : array
evaluate the estimated pdf on a provided set of points
kde(x0, x1,..., xd) : array
same as kde.eval_grid(x0, x1,..., xd)
Example
-------
>>> N = 100
>>> ei = np.random.normal(loc=0, scale=0.075, size=(N,))
>>> x = np.linspace(0, 1, N)
>>> import wafo.kdetools as wk
>>> y = 2*np.exp(-x**2/(2*0.3**2))+3*np.exp(-(x-1)**2/(2*0.7**2)) + ei
>>> kreg = wk.KRegression(x, y)
"""
def __init__(self, data, y, p=0, hs=None, kernel=None, alpha=0.0, xmin=None, xmax=None, inc=128, L2=None):
self.tkde = TKDE(data, hs, kernel, alpha, xmin, xmax, inc, L2)
self.y = y
self.p = p
def eval_grid_fast(self, *args, **kwds):
self._grdfun = self.tkde.eval_grid_fast
return self.tkde._eval_grid_fun(self._eval_gridfun, *args, **kwds)
def eval_grid(self, *args, **kwds):
self._grdfun = self.tkde.eval_grid
return self.tkde._eval_grid_fun(self._eval_gridfun, *args, **kwds)
def _eval_gridfun(self, *args, **kwds):
grdfun = self._grdfun
s0 = grdfun(*args, r=0)
t0 = grdfun(*args, r=0, y=self.y)
if self.p==0:
return t0 / s0
elif self.p==1:
s1 = grdfun(*args, r=1)
s2 = grdfun(*args, r=2)
t1 = grdfun(*args, r=1, y=self.y)
return (s2 * t0 -s1 * t1) / (s2 * s0 - s1**2)
__call__ = eval_grid_fast
class _Kernel(object):
def __init__(self, r=1.0, stats=None):
@ -956,6 +1040,8 @@ class Kernel(object):
def _get_name(self):
return self.kernel.__class__.__name__.replace('_Kernel', '').title()
name = property(_get_name)
def get_smoothing(self, *args, **kwds):
pass
def stats(self):
''' Return some 1D statistics of the kernel.
@ -1298,15 +1384,19 @@ class Kernel(object):
better for short tailed densities.
However, STT method in contrast to LCV is insensitive to outliers.
Example:
Example
-------
x = rndnorm(0,1,50,1);
hs = hstt(x,'gauss');
See also hste, hbcv, hboot, hos, hldpi, hlscv, hscv, kde, kdebin
See also
--------
hste, hbcv, hboot, hos, hldpi, hlscv, hscv, kde, kdebin
Reference:
Reference
---------
B. W. Silverman (1986)
'Density estimation for statistics and data analysis'
Chapman and Hall, pp 57--61
@ -2426,6 +2516,54 @@ def kde_demo3():
pylab.figure(0)
def kde_demo4(hs=None, fast=False):
N = 100
#ei = np.random.normal(loc=0, scale=0.075, size=(N,))
ei = np.array([-0.08508516, 0.10462496, 0.07694448, -0.03080661, 0.05777525,
0.06096313, -0.16572389, 0.01838912, -0.06251845, -0.09186784,
-0.04304887, -0.13365788, -0.0185279 , -0.07289167, 0.02319097,
0.06887854, -0.08938374, -0.15181813, 0.03307712, 0.08523183,
-0.0378058 , -0.06312874, 0.01485772, 0.06307944, -0.0632959 ,
0.18963205, 0.0369126 , -0.01485447, 0.04037722, 0.0085057 ,
-0.06912903, 0.02073998, 0.1174351 , 0.17599277, -0.06842139,
0.12587608, 0.07698113, -0.0032394 , -0.12045792, -0.03132877,
0.05047314, 0.02013453, 0.04080741, 0.00158392, 0.10237899,
-0.09069682, 0.09242174, -0.15445323, 0.09190278, 0.07138498,
0.03002497, 0.02495252, 0.01286942, 0.06449978, 0.03031802,
0.11754861, -0.02322272, 0.00455867, -0.02132251, 0.09119446,
-0.03210086, -0.06509545, 0.07306443, 0.04330647, 0.078111 ,
-0.04146907, 0.05705476, 0.02492201, -0.03200572, -0.02859788,
-0.05893749, 0.00089538, 0.0432551 , 0.04001474, 0.04888828,
-0.17708392, 0.16478644, 0.1171006 , 0.11664846, 0.01410477,
-0.12458953, -0.11692081, 0.0413047 , -0.09292439, -0.07042327,
0.14119701, -0.05114335, 0.04994696, -0.09520663, 0.04829406,
-0.01603065, -0.1933216 , 0.19352763, 0.11819496, 0.04567619,
-0.08348306, 0.00812816, -0.00908206, 0.14528945, 0.02901065])
x = np.linspace(0, 1, N)
y0 = 2*np.exp(-x**2/(2*0.3**2))+3*np.exp(-(x-1)**2/(2*0.7**2))
y = y0 + ei
kreg = KRegression(x, y, p=0, hs=hs)
kreg.tkde.kernel.get_smooting = kreg.tkde.kernel.hste
if fast:
kreg.__call__ = kreg.eval_grid_fast
f = kreg(output='plot', title='Kernel regression', plotflag=1)
pylab.figure(0)
f.plot(label='p=0')
kreg.p=1
f1 = kreg(output='plot', title='Kernel regression', plotflag=1)
f1.plot(label='p=1')
pylab.plot(x,y,'.', x,y0, 'k')
pylab.legend()
pylab.show()
print(kreg.tkde.tkde.inv_hs)
print(kreg.tkde.tkde.hs)
def test_docstrings():
import doctest
@ -2433,4 +2571,4 @@ def test_docstrings():
if __name__ == '__main__':
#test_docstrings()
kde_demo3()
kde_demo4()
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